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3 years ago

PLEASE HELP ME PLEASE LOL Solve for x and y. Round your answers to the nearest tenth.

Mathematics

2 answers:

trasher [3.6K]3 years ago

4 0

Answer:

Step-by-step explanation:

Pachacha [2.7K]3 years ago

4 0

Answer:

x ≈ 6.6, y ≈ 13.3

Step-by-step explanation:

Using the tangent ratio in the right triangle to find x

tan30° = $\frac{opposite}{adjacent}$ = $\frac{BC}{AB}$ = $\frac{x}{11.5}$ ( multiply both sides by 11.5 )

11.5 × tan30° = x , then

x ≈ 6.6 ( to the nearest tenth )

Using the cosine ratio in the right triangle to find y

cos30° = $\frac{adjacent}{hypotenuse}$ = $\frac{AB}{AC}$ = $\frac{11.5}{y}$ ( multiply both sides by y )

y × cos30° = 11.5 ( divide both sides by cos30° )

y = $\frac{11.5}{cos30}$ ≈ 13.3

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HELP ASAP PLZ i need help !<br>help me :((

kodGreya [7K]

Answer:

(1) $g[f(x)]=\frac{8x-1}{12x-4}$

(2) $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

Step-by-step explanation:

Given functions f(x) = (4x-1)

are $g(x)=\frac{2x+1}{3x-1}$

(1) $g[f(x)]=\frac{2(4x-1)+1}{3(4x-1)-1}$

$=\frac{8x-2+1}{12x-3-1}$

$=\frac{8x-1}{12x-4}$

(2) for $g^{-1}(x)$ , rewrite the function g(x) in terms of an equation

$y=\frac{2x+1}{3x-1}$

Substitute y in place of x and x in place of y, then solve for y.

$x=\frac{2y+1}{3y-1}$

(3y-1)x = 2y+1

3xy - x = 2y + 1

3xy - 2y = x + 1

y(3x-2) = x + 1

$y=(\frac{x+1}{3x-2} )$

⇒ $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $f[g(x)]=(x-1)$

$f[g(x)]=4[\frac{2x+1}{3x-1}] =(x-1)$

⇒ $\frac{(8x+4)-(3x-1)}{3x-1}=(x-1)$

⇒ $\frac{8x-3x+4+1}{3x-1}=(x-1)$

⇒ $\frac{5x+5}{(3x-1)}=(x-1)$

⇒ $5x+5=(3x-1)(x-1)$

⇒ $5x+5=3x^2-3x-x+1$

⇒ $5x+5=3x^2-4x+1$

⇒ $3x^2-9x-4=0$

⇒ $x=\frac{9\pm\sqrt{(-9)^2-4(-4)\times3} }{2\times3}$

$x=\frac{9\pm\sqrt{81+48} }{6}$

$x=\frac{9\pm\sqrt{129} }{6}$

$x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

4 0

3 years ago

4. The stock market goes up more often that it goes down. Assume the probability that the stock market goes up in a randomly sel

tekilochka [14]

Answer:

a: 0.0022

b: 0.00002

c: 0.0002

d: 924

e: 0.0025

f: 0.6652

g: Expected value 7.8 months, standard deviation 1.77 months

Step-by-step explanation:

This is a binomial situation. Either the market goes up, or it doesn't. (It could stay the same, but it doesn't offer that as an option, so we don't include it).

When calculating probability of a binomial situation, use the formula

(nCr)(p^r)(q^(n-r)) where p is the probability of success, q is the probabilty of failure, n is the the number of times the situation occurs, and r is the desired number of successful outcomes. The function nCr tells us how many ways you can choose r items from n total items. In this case, we are choosing some number of months, r, from 12 months, n

For our situation we have: n = 12, r = 12, p = 0.6, q = 0.4,

For a: (12C12)(0.6^12)(0.4^0) = (1)(0.0022)(1) = 0.0022

We want all 12 months of success and no months of failure

For b: (12C0)(0.6^0)(0.4^12) = (1)(1)(0.00002) = 0.00002

We want all months of failure, and no months of success

For c: (0.6^6)(0.4^6) = 0.0002

We don't need the nCr function because it tells us that it we want 6 months of success followed by 6 months of failure. There's only 1 way to do that, so there's nothing to count

For d: 12C6 = 924

There are 924 different ways to the market can go up 6 times out of 12 months

For e: (12C2)(0.6^2)(0.4^10) = (66)(0.36)(0.0001) = 0.0025

For f: Add the following probabilities together...

(12C7)(0.6^7)(q^5) + (12C8)(0.6^8)(q^4) + (12C9)(0.6^9)(q^3)

+ (12C10)(0.6^10)(q^2) + (12C11)(0.6^11)(q^1) + (12C12)(0.6^12)(q^0)

= 0.6652

They are mutually exclusive, the probability for the union is zero because they can't happen at the same time

For g: Find expected value with the formula E = np , here n = 12, p = 0.6, so

E = 12(0.6) = 7.8 months

Find the standard deviation with the formula s = √(npq), or s = √(Eq), here q = 0.4, so s = √(7.8(0.4)) = 1.77 months

7 0

3 years ago

The cross-sectional areas of a right pyramid and a right cylinder are congruent. The pyramid has a height of five units, and a r

Mazyrski [523]

Answer:

the volume of the right cylinder is 1.8 times the volume of the pyramid

Step-by-step explanation:

The volume of a pyramid is

$V = \dfrac{1}{3} \times B\times H$

where the height of the pyramid is 5

$V = \dfrac{1}{3} \times B\times 5$

$V = \dfrac{5}{3} B \ units ^3$

On the other hand, the volume of a right cylinder is

V = BH

where the height of the right cylinder = 3 units

V = 3 B units³

Since we know that the cross-sectional areas are congruent, comparing the two-volume, we have the ratio of their volumes to be:

$\dfrac{V_p}{V_c}= \dfrac{\dfrac{5}{3}B}{3B}$

$\dfrac{V_p}{V_c}= \dfrac{5}{9}$

$9 V_p = 5 V_c$

$V_c = 1.8 \ V_p$

Hence, the volume of the right cylinder is 1.8 times the volume of the pyramid

6 0

2 years ago

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more

lyudmila [28]

Answer:

Jersey cost $8 and pair of shorts $5

Step-by-step explanation:

There are several ways to solve this, but I will find the solution using the system of equations.

Let's mark price of jersey with x, and price of pair of shorts with y. That means:

12x + 12y = 156

4x + 6y = 62

Now, we can multiply the second equation with -2 to cancel out y:

12x + 12y = 156

-8x - 12y = -124

That only leaves us with:

12x - 8x = 156 - 124

4x = 32

x = $8

Now we plug the value for x into any equation to find y:

4x + 6y = 62

32 + 6y = 62

6y = 30

y = $5

6 0

2 years ago

Read 2 more answers

A family has 5 children. Compute the probabilities of the following events:

Arlecino [84]

I think the answer is 10% and 90%

4 0

3 years ago

Read 2 more answers